Electrophoresis   

Goals for this  unit:

1. Understand essential theoretical concepts of movement of a charged particle in an electric field.

2. Know types of media commonly used for electrophoresis and the difference between zonal and boundary methods

3. Be familiar with common applications:

•      PAGE   /  Ferguson plots
•      Nucleic Acid methods (sequencing gels / Southern blots)
•      SDS PAGE (theory and practice - DISC gels)
•      IEF gels   (2D - gels)

4. Other Practical Aspects (tracking dyes / staining ) 

     (Some of the electrophoresis notes given below are modified in part from notes by Terry Frey - San Diego State Univ.)

I. Theory: (Note: While many of these theoretical concepts may not seem too useful in electrophoresis, many of the concepts (limiting velocity, frictional coefficient, Stokes radius, etc.) are very similar to those we will using in the next unit on sedimentation.)

  A. Macromolecule accelerated by a force 

1. F = q E  (q = net charge on molecule; E is the electric field strength).
2. Force causes an acceleration  (recall  Force = mass x acceleration;  F = ma). 
3. Limiting Velocity: movement in a liquid is resisted by a frictional force (viscous drag) that is proportional to the velocity.

               F_f  = f v  ( f = frictional coefficient);  when F_f  = -F, no more acceleration 

                                    ==> molecule has reached its limiting velocity.

   4. Define a mobility per unit field, U

   5. Stokes Law: For a spherical molecule of radius, r, and charge z e (e = elementary charge, charge on 1 electron)

            where r_h is the radius of a sphere of equal volume, and h is viscosity (~0.01g/cm-sec).

  B. Rigorous quantitative treatment is very difficult:

Electric field actually felt by the macromolecule is difficult to evaluate due to the fact that the macromolecule is a very large ion in solution with many small counterions. Extreme situations:

1. Very Low Ionic Strength
   
   Once the macromolecule is separated slightly from its counterions, it takes enormous energy to pull them further apart ==> charge separation counteracts the external field resulting in little or no molecular transport.
2. Very High Ionic Strength -- overcomes the problem of charge separation (the macromolecule will always have enough counterions around). But this creates an ion cloud around the particle partially shielding it from the external field. This does not prevent electrophoretic movement, but it does complicate rigorous analytical treatment.
3. Most electrophoretic experiments (whether preparative or analytical) are analyzed semi-empirically.

II. Experimental Approaches:

  A. Media -- Three common types

1. Starch Gel -- swollen potato starch granules (used for prep isoelectric focusing)
2. Agarose Gel -- purified large MW polysaccharide (from agar) ==> very open (large pore) gel used frequently for large DNA molecules
3. Polyacrylamide Gels -- most commonly used gel because they are very stable and can be made at a wide variety of concentrations or even with a gradient of concentrations ==> large variety of pore sizes
                   
4. Acrylamide Concentrations -- typically 5-20% by weight (5%, 7.5%, 10%, 12.5%, 15%, 20% common) ==> gel is mostly water. Acrylamide polymerizes in head-to-tail fashion to form long polymers which form a complex network held together by bis-acrylamide crosslinks. The cris-crossing polymers create pores in the gel; the size of pores is determined by the acrylamide concentraion.
5. Acrylamide can be polymerized into any desired shape -- two shapes used for electrophoresis

   1. Tube Gels -- polymerize in glass tubing ==> cylindrical shape
   2. Slab Gels -- polymerize between glass plates

  B.  Boundary and Zonal (~ sedimentaiton)

1. Boundary:  measure the rate of movement of the boundary and calculate U from E and v -- rarely used
   
2. Zonal: (~zonal sedimentation; ~ sucrose density gradients)

   1. sample is applied in a zone (small region: a spot on moistened paper or a band on a gel) and an applied field causes the molecules to separate into zones based upon different U's.
   2. need some way of stabilizing the zones to prevent mechanical mixing (from vibrations) or convection mixing (from temperature differences -- a particularly severe problem with resistance heating caused by the electric field).

               For example - Paper Electrophoresis

   1. a strip of paper is kept moist with buffer to make it electrically conductive; ends are dipped into buffer solutions containing electrodes across which an electric potential is applied
   2. Used primarily for separation of small molecules ==> must use a high voltage, otherwise they diffuse too rapidly ==> paper must be cooled (usually by water)

III. Common Applications 

   A. PAGE / Ferguson Plots  

            Log relative mobility vs. % Gel conc.  log U = log U^o - K[C]

   B. Nucleic Acid Methods -- How does a gel affect mobility?

Consider simple (conformationally) molecules moving free in solution in the presence of an electric field.

1. Structure -- Random coil of...
   Thus: Z is proportional to the number of nucleotides and thus M (molecular weight).
                 Recall that for an ellipsoid: f = 6 p h r_h F and:       
                 ==> f is proportional to M (for molecules with similar shapes)
       --> both numerator and denominator contain terms directly proportional to M 

                ==> M terms cancel out and the electrophoretic mobility

                ==>  U, should be ~ independent of the size of the nucleic acid.

        (N. Davidson at CalTech measured U for nucleic acids without a supporting gel, and found that it is constant from 1 nucleotide up to 1.7 x 10⁵ nucleotides!)

    2. How can we use electrophoresis to separate molecules? 

             ==>   Do Electrophoresis in a gel matrix -- the gel sieves the molecules

• large molecules move slowly because they have difficulty going through the pore

• small molecules move rapidly because their freedom is not restricted

• How is pore size related to gel concentration?  We can adjust the gel concentration to produce a pore size appropriate for the sizes of molecules we wish to separate.
• 7.5%  (45K-400K) / 10% (22K-300K)  /  12% (13K-200K)   /  15% (2.5K-100K)
  

U is measured as the "relative" distance traveled, R_f = R / R_max
Experimentally, we find that R_f depends upon log M 

      ==> R_f = b - a log M where "a" and "b" are constants determined (primarily) by the gel; they're measured empirically by plotting R_f for molecules of known M and making a calibration curve.  Note: the relationship is linear only over a limited range of log M. 

                

1. Agarose:  0.2 % for Nucleic Acids up to M = 150 x 10⁶
                      0.8 % for Nucleic Acids up to M = 50 x 10⁶
2. Polyacrylamide: for smaller Nucleic Acids; choose % acrylamide to produce correct size pore

     4. Common Applications - sequencing gels (Fig 1, Fig 2)  /  Southern blots (see animation 2)

  C. Electrophoresis of Proteins - Advantages of SDS PAGE

1. Less straightforward because charge on proteins is much more variable -- it depends upon:

   1. amino acids composition
   2. pH;
   3. net charge can be + or - or 0

2. Electrophoresis of "native" proteins is relatively rare except for Isoelectric Focusing described later.  

           What is needed is a way of modifying proteins so z is proportional to M (as is the case with nucleic acids).

1. Sodium Dodecyl Sulfate = Sodium Lauryl Sulfate: CH₃(CH₂)₁₁SO₃^- Na⁺
   A detergent that contains a hydrophobic tail region [ CH₃(CH₂)₁₁ ], attached to a hydrophilic group, SO₃^- Na⁺, making it amphipathic. It is a very strong detergent which denatures proteins by binding to the polypeptide backbone.
2. Measurements show that most proteins bind 1.4 gm SDS/gm protein with very little variation (except for some membrane proteins; membrane proteins are very hydrophobic and may bind more SDS) 

==> The charge on an SDS-protein complex is determined almost entirely by SDS --> -1 charge for each SDS. Since the amount of SDS bound is determined by the size of the protein and all protein/SDS micelles are anionic ==> z is directly proportional to M

Hydrodynamic studies show that the shape of an SDS/protein complex is a rod or prolate ellipsoid of ~18Å diameter and a length proportional to M

               Electrophoresis of SDS/protein micelles through a polyacrylamide gel should separate them according to M (~ nucleic acids) ==> R_f = b - a log M

If one plots the mobility for different proteins as a function of gel concentration, a Ferguson Plot, one finds that the mobilities of all proteins extrapolate to the same value at [gel conc.] = 0 as expected. The slope of the mobility of a single protein provides another more accurate method of estimating its molecular weight from SDS PAGE.

   Discontinuous Electrophoresis (Disc): Most common type of SDS-PAGE

1. Buffers--2 layers: upper layer contains low mobility ions;   lower layer contains high mobility ions
2. The two zones move down with a sharp boundary between them. Why? Should not the faster, lower buffer ions should move further ahead, leaving slow ones behind?   But -

They experience different potentials: V_U  >>  V_L

Ohms Law: V = R i: i = current and is the same for both layers, R is the resistance.  R_U  >>  R_L, because:
                                    
where c_i = concentration; m_i = mobility; z_i= charge on the ith ion. ==> R_U >> R_L because m_U is smaller than m_L

Thus, if c_U and c_L are chosen appropriately, V_U will be enough larger than V_L to compensate for lower mobility of ions in the upper zone 

                     ==> 2 zones move at the same speed with a sharp boundry between them.
                                      .

Why a sharp boundry? (1) if a mobile lower zone ion drifts into the upper zone, it immediately experiences a higher potential, V_U, and speeds up until it reaches the lower zone where the lower potential, V_L, causes it to slow down again. (2) if a low mobility upper zone ion drifts into the lower zone, it immediately experiences a lower potential, V_L, which causes it to slow down until it drifts back into the upper zone.

What about proteins? Choose upper and lower zone ions so that:      m_U < m_proteins /SDS  < m_L

                        _{Cl-   vs.  proteins / SDS   vs.  Gly  [mobility of Gly varies with pH;  (pH 6.7, Gly ~0  /  > pH 9.0, Gly ~ -1)]}

                Upper "stacking gel" -   proteins / SDS  >  Gly ~(0)

                Lower "running gel"    -   Gly ~(-)  >  proteins / SDS
==> proteins will be concentrated at the interface into thin zones stacked in order of protein mobility. Note: all this assumes electrophoresis in a "stacking" gel with large pores which do not inhibit protein movement. 

                            

When the thin bands of proteins reach the "separating" gel, their mobility decreases dramatically and the upper buffer ions pass them. At this point, the proteins are separated according to their individual mobilities (sizes). The whole point of this buffer system is to concentrate the proteins into very thin zones before separating them.

     Common SDS page protocol / web info on SDS PAGE technique

  D. Isoelectric Focusing:

All protein carry charges that vary from a net positive charge at low pH (-COOH and -NH₃⁺ forms of acidic and basic functional groups), through 0 at some intermediate pH, to a net negative charge (-COO^- and -NH₂ forms) at high pH.

1. pI - Isoelectric Point:  pH at which a protein has a net 0 charge (positive and negative charges balance). Depends mostly on the amino acid composition and a little on the tertiary structure
2. Create a pH gradient in a gel: Can be done on a slab (vertical or horizontal) or a tube.
   (~ Equilibrium Density Gradient Centrifugation (IsoPycnic Centrifugation))
3. The final positions of each band depend only on an intrinsic property of the proteins, their pI's, and not on where they started in the gel or their mobility to reach the pI region.
4. How to make a stable pH gradient? Must have a buffer for each pH along the gradient
   ==> Ampholytes (various commercial names) are small organic molecules with different combinations of acidic and basic groups so that each one has a different pKa. If one electrophoreses a mixture of ampholytes (polyampholytes) with H₃PO₄ in the Anode buffer reservoir (to buffer at very low pH) and NaOH in the Cathode buffer reservoir (to buffer at very high pH), each ampholyte will migrate to a pH equal to its pKa and buffer the pH at that point.

  2D Electrophoresis: combine 2 types of electrophoresis

1. Most common: combine Isoelectric Focusing in tube gels and SDS-PAGE in slab gels
   Final gel has a complex mixture or proteins separated by pI along the horizontal axis and by log M along the vertical axis. Can resolve thousands of spots (proteins) by this technique. Analysis is now automated by computer so that one can do 2D gels on whole cell extracts and monitor how each protein changes during: a) Development; b) Transformation; c) Excitation -- e.g. by a hormone etc.

1. SDS-PAGE -- non-reducing conditions (-S--S- bonds intact) + reducing conditions

V. Other Practical Aspects (dyes and stains)

          Tracking Dye [ bromophenol blue (+) / methylgreen (-) ]

          Staining   [ Coomassie Blue  /  Silver   /   SYPRO orange  / Ethidium bromide]